Product Details

• Amazon Sales Rank: #85462 in Books
• Published on: 2005-07-21
• Original language: English
• Number of items: 1
• Binding: Paperback
• 172 pages

Review
"Among the many expositions of Godel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstanding and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature" - John W. Dawson, Jr., author of Logical Dilemmas: The Life and Work of Kurl Godel Godel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths... It plays a part in modern linguistic theories, which emphasize the power of language to come up with new ways to express ideas. And it has been taken to imply that you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself. - An Incomplete Education, by Judy Jones and William Wilson"

Synopsis
The theorem is tossed about and misapplied by the uninformed, so the author gathered up quotes and responses he's been involved with on the internet and tackled a presentation for what he terms a "general audience." Mathematicians will turn to more sophisticated treatments; determined non-mathematicians with a strong bent for formal logic will be a

About the Author
A philosopher by training (PhD, University of Stockholm), Torkel Franzen has for the past twenty years been active working in computer science (at the Swedish Institute of Computer Science). He is the author of a number of books, among them Inexhaustibility: A Non-Exhaustive Treatment.

Customer Reviews

Bit overpriced but the really the best guide out there
Godel's theorem is tossed about with wild abandon, particularly by people who don't really understand it - and I certainly would not claim to understand all it's subtleties - and this is a great little book to help you clear some of the fog. It is worth noting that Godel's theorem is quite limited in practical import, a large number of the theories in Mathematics do not fit the criteria for Godel's theorem and one can safely say that Physics has far from complete in terms of working out the consequences of its theories. For example there is a million dollars waiting for you if you can mathematically prove there is mass in the universe.

A quick example of the sort of things that this book helps to make clear. For ages I didn't understand the flaw in the standard philosophical argument about how Godel's theorem "shows" that you can "know" a statement is true but not prove it... I always thought it was due to the lack of non-contradiction between the statement and the axioms but somehow this didn't seem to work. The claim is that as Godel's theorem states that if T is a consistent theory then there is a statement P that says it cannot be proved within T. Well it must be true because otherwise there would be a proof! Simple right? Well no, because it is only true if T is consistent which of course you can't.... worth the price just for clarifying that.